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Algorithmic Thinking A Problem Based Introduction 1st Edition by Daniel Zingaro 1718500807 9781718500808

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Algorithmic Thinking A Problem Based Introduction 1st Edition Daniel Zingaro Digital Instant Download

Author(s): Daniel Zingaro
ISBN(s): 9781718500808, 1718500807
Edition: 1
File Details: PDF, 4.09 MB
Year: 2020
Language: english
SKU: EB-34803990 Category: Tag:

Algorithmic Thinking A Problem Based Introduction 1st Edition by Daniel Zingaro – Ebook PDF Instant Download/Delivery: 1718500807, 9781718500808

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ISBN 10: 1718500807

ISBN 13: 9781718500808

Author: Daniel Zingaro

Algorithmic Thinking will teach you how to solve challenging programming problems and design your own algorithms. Daniel Zingaro, a master teacher, draws his examples from world-class programming competitions like USACO and IOI. You’ll learn how to classify problems, choose data structures, and identify appropriate algorithms. You’ll also learn how your choice of data structure, whether a hash table, heap, or tree, can affect runtime and speed up your algorithms; and how to adopt powerful strategies like recursion, dynamic programming, and binary search to solve challenging problems.

Line-by-line breakdowns of the code will teach you how to use algorithms and data structures like:

  • The breadth-first search algorithm to find the optimal way to play a board game or find the best way to translate a book
  • Dijkstra’s algorithm to determine how many mice can exit a maze or the number of fastest routes between two locations
  • The union-find data structure to answer questions about connections in a social network or determine who are friends or enemies
  • The heap data structure to determine the amount of money given away in a promotion
  • The hash-table data structure to determine whether snowflakes are unique or identify compound words in a dictionary

NOTE: Each problem in this book is available on a programming-judge website. You’ll find the site’s URL and problem ID in the description. What’s better than a free correctness check?

Algorithmic Thinking A Problem Based Introduction 1st Table of contents:

1 Hash Tables
Problem 1: Unique Snowflakes
The Problem
Simplifying the Problem
Solving the Core Problem
Solution 1: Pairwise Comparisons
Solution 2: Doing Less Work
Hash Tables
Hash Table Design
Why Use Hash Tables?
Problem 2: Compound Words
The Problem
Identifying Compound Words
Solution
Problem 3: Spelling Check: Deleting a Letter
The Problem
Thinking About Hash Tables
An Ad Hoc Solution
Summary
Notes

2 Trees and Recursion
Problem 1: Halloween Haul
The Problem
Binary Trees
Solving the Sample Instance
Representing Binary Trees
Collecting All the Candy
A Completely Different Solution
Walking the Minimum Number of Streets
Reading the Input
Why Use Recursion?
Problem 2: Descendant Distance
The Problem
Reading the Input
Number of Descendants from One Node
Number of Descendants from All Nodes
Sorting Nodes
Outputting the Information
The main Function
Summary
Notes

3 Memoization and Dynamic Programming
Problem 1: Burger Fervor
The Problem
Forming a Plan
Characterizing Optimal Solutions
Solution 1: Recursion
Solution 2: Memoization
Solution 3: Dynamic Programming
Memoization and Dynamic Programming
Step 1: Structure of Optimal Solutions
Step 2: Recursive Solution
Step 3: Memoization
Step 4: Dynamic Programming
Problem 2: Moneygrubbers
The Problem
Characterizing Optimal Solutions
Solution 1: Recursion
The main Function
Solution 2: Memoization
Problem 3: Hockey Rivalry
The Problem
About Rivalries
Characterizing Optimal Solutions
Solution 1: Recursion
Solution 2: Memoization
Solution 3: Dynamic Programming
A Space Optimization
Problem 4: Ways to Pass
The Problem
Solution: Memoization
Summary
Notes

4 Graphs and Breadth-First Search
Problem 1: Knight Chase
The Problem
Moving Optimally
Best Knight Outcome
The Knight Flip-Flop
A Time Optimization
Graphs and BFS
What Are Graphs?
Graphs vs. Trees
BFS on Graphs
Problem 2: Rope Climb
The Problem
Solution 1: Finding the Moves
Solution 2: A Remodel
Problem 3: Book Translation
The Problem
Building the Graph
The BFS
Total Cost
Summary
Notes

5 Shortest Paths in Weighted Graphs
Problem 1: Mice Maze
The Problem
Moving On from BFS
Shortest Paths in Weighted Graphs
Building the Graph
Implementing Dijkstra’s Algorithm
Two Optimizations
Dijkstra’s Algorithm
Runtime of Dijkstra’s Algorithm
Negative-weight Edges
Problem 2: Grandma Planner
The Problem
Adjacency Matrix
Building the Graph
Weird Paths
Task 1: Shortest Paths
Task 2: Number of Shortest Paths
Summary
Notes

6 Binary Search
Problem 1: Feeding Ants
The Problem
A New Flavor of Tree Problem
Reading the Input
Testing Feasibility
Searching for a Solution
Binary Search
Runtime of Binary Search
Determining Feasibility
Searching a Sorted Array
Problem 2: River Jump
The Problem
A Greedy Idea
Testing Feasibility
Searching for a Solution
Reading the Input
Problem 3: Living Quality
The Problem
Sorting Every Rectangle
Binary Search
Testing Feasibility
Testing Feasibility More Quickly
Problem 4: Cave Doors
The Problem
Solving a Subtask
Using a Linear Search
Using Binary Search
Summary
Notes

7 Heaps and Segment Trees
Problem 1: Supermarket Promotion
The Problem
Solution 1: Maximum and Minimum in an Array
Max-Heaps
Min-Heaps
Solution 2: Heaps
Heaps
Two More Applications
Choosing a Data Structure
Problem 2: Building Treaps
The Problem
Recursively Outputting Treaps
Sorting by Label
Solution 1: Recursion
Range Maximum Queries
Segment Trees
Solution 2: Segment Trees
Segment Trees
Problem 3: Two Sum
The Problem
Filling the Segment Tree
Querying the Segment Tree
Updating the Segment Tree
The Main Function
Summary
Notes

8 Union-Find and Disjoint Sets
Problem 1: Social Network
The Problem
Modeling as a Graph
Solution 1: BFS
Union-Find
Solution 2: Union-Find
Optimization 1: Union by Size
Optimization 2: Path Compression
Union-Find
Relationships: Three Requirements
Choosing Union-Find
Optimizations
Problem 2: Friends and Enemies
The Problem
Augmentation: Enemies
The main Function
Find and Union
SetFriends and SetEnemies
AreFriends and AreEnemies
Problem 3: Drawer Chore
The Problem
Equivalent Drawers
The main Function
Find and Union
Summary
Notes

Afterword
A Algorithm Runtime
The Case for Timing … and Something Else
Big O Notation
Linear Time
Constant Time
Another Example
Quadratic Time
Big O in This Book

B Because I Can’t Resist
Unique Snowflakes: Implicit Linked Lists
Burger Fervor: Reconstructing a Solution
Knight Chase: Encoding Moves
Dijkstra’s Algorithm: Using a Heap
Mice Maze: Tracing with Heaps
Mice Maze: Implementation with Heaps
Compressing Path Compression
Step 1: No More Ternary If
Step 2: Cleaner Assignment Operator
Step 3: Understand the Recursion

C Problem Credits

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